In animals, piRNAs direct PIWI-clade Argonaute proteins to slice complementary transposon transcripts. Transposons can evade silencing through target site mutations. We report that PIWIs efficiently cleave transcripts only partially paired to their piRNA guide. Measurements of mouse PIWI protein affinity and cleavage rates for thousands of RNAs in vitro and in vivo show that PIWI slicing tolerates mismatches to any target nucleotide, including those flanking the scissile phosphate. Although piRNA 5' terminal nucleotides accelerate target finding, they are dispensable for binding or catalysis, unlike AGO-clade Argonautes, which require uninterrupted siRNA:target pairing from the seed to the nucleotides past the scissile bond. PIWIs are thus better equipped than AGOs to target newly acquired or rapidly diverging endogenous transposons without recourse to novel small RNA guides.